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CHAPTER III. THE ELEMENTS OF ANCIENT GRAVITATIONAL ASTRONOMY. Section I.—The pyramid’s external definition of the earth and its orbit.
Professor Petrie’s admirable survey data for the Great Pyramid are so comprehensive and accurate as to enable us to settle three momentous questions. These questions, which are closely inter-related, may be expressed as follows :— (1) How far the existing measurements give evidence concerning the designer’s intentions, To form the necessary basis for the analytical investigation for the above, Petrie’s system of Survey Co-ordinates has had to be converted into an equivalent system of co-ordinates oriented with respect to the mean azimuth1 of the Great Pyramid. All the necessary data—Petrie’s original: co-ordinates and the new equivalent Pyramid azimuth co-ordinates—are given in relation on Plate XIX, to enable the mathematical reader to check the conversion for himself. Subtraction of related co-ordinate units of Plate XIX—i.e. for coordinates from the same base and on the same straight line—and conversion of the units into British inches give all the Pyramid’s true azimuth base distances shown on Plate XX. Plate XX also shows Petrie’s oblique distances between base points and diagonal corners of sockets. The latter distances are not stated with reference to any common azimuth. They are nothing more, in each case, than the direct distance in a straight line between two stated points. In this form, Petrie’s distances are not a suitable basis for the analytical investigation of all the related data.
¶ 142. THE SIGNIFICANCE OF PETRIE’S PYRAMID BASE DISTANCES. In one application, however, Petrie’s base distances are of direct value for analysis. They determine the existing form of the square defining the central extent of base hollowing-in. This is the square RQPS on Plate XX. The North side, QP, of this square = 9069.4 B”, and defines the line of CD where casing was found and surveyed. The East side, PS, of this square = 9067.7 B”, and defines the line of EF where casing was found and surveyed. The South side, RS, of this square = 9069.5 B”, and defines the line of GH where casing was found and surveyed. The West side, RQ, of this square = 9068.6 B”, and defines the line of BA where casing was found and surveyed. The close agreement of the North and South measurements, 9069.4 and 9069.5 B” respectively, and the variation of 0.9 B” between the East side (9067.7 B”) and the West side (9068.6 B”) suggest --- (1) That the North and South measures define the intended or original value as 9069.5 B” ; and
For a larger rotated version click here:
Now if the slightly shorter distance between the North and South base sides, as compared with the distance between the East and West base sides, is due to the subsidence effect inferred, the Great Pyramid should contain the following indications of such subsidence :— (1) The courses of the Pyramid masonry should indicate a slight dip inwards, towards the centre. Every one of the five indications outlined are defined by the existing state of the Great Pyramid’s masonry as surveyed and measured by Professor Petrie. The external and internal evidences of subsidence are discussed in detail in Sections II and III of this Chapter.
Petrie has shown that the four corner sockets of the Great Pyramid were primarily cut to fix the alignments of the two diagonals of the Pyramid base. In three cases the alignments of the diagonals are fixed by the outer corner of each of three sockets, L, K, and M, for the N.W., N.E., and S.E. sockets respectively, as figured on Plate XX. In the case of the S.W. socket, the socket surface was carried to UX, 17½ inches to the West of the point Z on the diagonal ZK. The point Z, defining the diagonal alignment is, however, indicated by a chiselled line WZ cut by the original workers for this purpose. As shown on Plate XX, the true East to West distance from East side of S.E. socket to West side of S.W. socket—i.e. between M and the line UX produced—is 9140.63 B”. Petrie gives the oblique distance XM as 9141.4 B”. Now the true geometrical Pyramid base side The existing distance is 0.47 B” shorter than the true distance. In the same way the sum of the true azimuth co-ordinates between AB and EF (Plate XX), at the centre of the base, is 9068.83 B” or 0.62 B” shorter than the mean of the measurements indicated as original by the distorted oblique distances QP and RS, 9069.4 and 9069.5 B” respectively. (¶ 142.) The shortening effect on base measurements due to subsidence would naturally be greatest across the centre between two opposite base sides. In consequence, we may take the shortening of North base as not greater than the mean of the other two variations noted, For a larger rotated version click here:
¶ 145. THE ORIGINAL SETTING-OUT LINES OF THE PYRAMID BASE. As stated by Petrie, the existing definition of the base diagonals - owing to subsidence distortion - does not give precisely rectangular diagonals. The amount of error from true rectangular diagonals is shown by the azimuth co-ordinates of the half diagonals of Plate XX. The intentional or original setting out can be very closely approximated by taking the existing North base socket distance LK (+ its correction of ¶144, i.e. 0.54 B”) and the existing South base socket distance ZM (+ its correction of ¶ 144, i.e. 0.47 B”), and by taking O the centre of the base as fixed ; then with these as data we can correct the angles LOK and ZOM each to a right angle, to give the closely approximate true original socket corners L, K, M, and Z. The result is that the half diagonals OL, OK, OM, and OZ to the socket corners L, K, M, and Z respectively, are defined by four true squares respectively of length of side 4567.41 B”, 4562.10 B”, 4570.55 B”, and 4553.05 B”. The result is confirmed, not only as to its supplying the original intention, but as to its definition of the original construction, by the S.E. socket corner M becoming the precise corner of the Pyramid square base of 36524.25 P” circuit. The azimuth distance between UX produced and the S.E. socket corner M is also the length of the base side for the Pyramid circuit 36524.25 P”. The Pyramid was therefore set out in preliminary lines as follows :—
Remembering that Professor Petrie’s reconstruction defines the hollowing-in of the core without applying the same feature to the casing, and that the new reconstruction, adopted in the present work, applies the hollowing-in to the casing, the reader will find instructive matter in the details of Plates XXI and XXII. These show the appearance of the South-East corner casing stone according to the two different reconstructions. It should be understood that Petrie carries down the masonry of the corner casing stones to the socket floors in all cases. The discovery of the Lisht Pyramid sockets and their foundation deposits (refer Section III, ¶197a) may have caused Professor Petrie to modify his reconstruction in this detail. But even this modification could scarcely redeem the evident weakness of his reconstruction as applied to the South-East socket corner casing stone. A reconstruction stands or falls under its critical application to detail. Apart, then, from the identities established concerning the intentional circuit of the Pyramid’s base, we are assured that a critical technical examination of the two reconstructions, as applied to the detail of Plates XXI ‘ and XXII, will settle the matter conclusively, to the satisfaction of the thesis advanced in the present work.
The nett effect of the correction of the right angles of the base diagonals in ¶ 145 is as follows : — (1) That subsidence effect has reduced the true azimuth distance between the centres of the East and West casing base sides by the total amount of 0.67 inch. These corrections applied to the distances between the hollowed-in base sides give a constant distance of 9069.5 B”, East and West, or North and South, between centres of base sides. The East to West distance given by the existing slightly distorted features of the North’ and South base sides, as surveyed by Professor Petrie, still gives this value (¶ 142). This indicates that the Pyramid masonry, in centrally sliding slightly inwards, could not very appreciably reduce its external base length owing to the tightly fitting blocks. Externally it compromised by slightly skewing the external form of its base to retain its external base length practically unaltered, and at the same time produce the necessary diminution of azimuth co-ordinates to satisfy the subsidence conditions. This distortion of the external form of the Pyramid base bears relation to the distortion of the socket base only as effect to cause. All the data, then, at our disposal combine to show that the external corner to corner measures of the Pyramid remained practically unaltered, although very slightly skewed in direction. At the same time, the effect of the subsidence brought the hollowed-in central portion of the North base and of the South base in each case i inch nearer the centre of the Pyramid (¶ 147, Case 2) ; and in the case of the East and West sides 1/3 inch nearer the centre of the Pyramid (¶ 147, Case 1). In consequence, the hollowing-in extent of about 36” would be increased by subsidence to 37” on North and South base sides, and to 36-1/3” on East and West base sides. 37” is the value obtained by Professor Petrie from his sightings down the North face slope of the core masonry. This agrees with the value deduced for the North face including subsidence effect.
¶ 148. THE PYRAMID’S DISPLACEMENT FACTOR. Criticism, therefore, has shown that the Pyramid was set out to a base line of 9141.1 B”, that its distance between centres of opposite base sides was 9069.5 B”, and, independently, that its base sides were centrally hollowed to the extent of about 36”. The difference between the first two values, 9141.1 and 9069.5 B”, gives twice the extent of hollowing-in as 71.6 B”, and therefore the hollowing-in as 35.8 B”=35.76 P”. The actual Pyramid base circuit is therefore defined by two squares, one marginally 35.76 P” internal to the other. The outer square, defining the base corners, is 36,524.24 P” circuit, and the inner square is 8 × 35.76 P” (or 286.1 P”) less in circuit than the outer square. Now 286.1 P” (286.4 B”) is an important geometrical value of the Pyramid. It is also the measurement of the displacement of the North to South Vertical Axial Plane of the Pyramid’s Passage System Eastwards from the North to South Central Vertical Plane of the Pyramid. The existing displacement of the Passage System, as defined, was measured by Professor Petrie as follows : —
Plates XXIII, XXIV, and XXV (Figs. A, A1, and A2) show how the hollowed-in base feature, the 35th course axis, and the displacement of the Passage System are all geometrical functions of a composite system of geometry featuring the solar year to the scale of 10 P” to a day, and to the scale of 100 P” to a day. To convey the full significance of this to the reader it is necessary first to define the precise value of the solar year intentionally identified with the Pyramid’s base square circuit.
In ¶¶ 102-104 it was shown that the period of 25,826½ years was identified with the period of the Precession of the Equinoxes. In ¶ 102 it was explained that 78½ Phoenix cycles gave the identity 25,826½ Phoenix years (or intercalated Calendar years) = 25,826.54+ Solar years. Accurately, the identity defines the precise numerical values of the Pyramid’s base diagonals and of the base square circuit as follows :— (1) INITIAL HALF PHOENIX CYCLE.
(4) PYRAMID BASE CIRCUIT AND DIAGONALS. Let N = No. of days in solar year, and
Solving the simultaneous equations I and II, we get N =365.2424650 days. Then, Pyramid base circuit = 36,524.2465 P”, These are the values adopted for the geometrical representation developed in Plates XXIII, XXIV, and XXV. For a larger version click here:
It has been suggested by the evidence discussed in the two preceding chapters that the external features of the Great Pyramid were intended to form a geometrical representation of the dimensions and motions of the Earth and its orbit (¶114). Any such representation must, of necessity, be made with reference to a plane representing the plane of the Earth’s orbit. The plane of the Great Pyramid pavement is defined as this natural plane, as it is the plane of the Pyramid’s base square, defining the circuit of the solar year. For the necessary geometrical representation the Great Pyramid’s base plane, therefore, represents the plane of the Earth’s orbit. This, then, is the natural plane for the geometrical and comparative representation of all values defining the dimensions and motions of the Earth and its orbit. These values, in consequence, need only be looked for in relation to the Pyramid’s external features as defined in plan.
Consideration of the Earth’s motion in its orbit is complicated by several factors. These complications, however, make it a considerably easier matter to specify the intention of any geometrical representation of the elements of the Earth and its orbit. One of the complications referred to is that there are three different year values defining the revolution of the Earth round its orbit. These are the Solar (or Tropical) year, the Sidereal (or Stellar) year, and the Anomalistic (or Orbital year). The Solar year is slightly less than 365¼ days, the Sidereal year is slightly more than 365¼ days, and the Anomalistic year is slightly longer than the Sidereal year. Were the Earth’s axis rigidly constant in its inclination, and in the direction of its inclination, the Solar year would be of the same length as the Sidereal year. Were the plane and axes of the Earth’s orbit rigidly fixed in relation to the fixed stars, the Anomalistic year would also be of the same length as the Sidereal year. The Solar and Anomalistic years are therefore departures from the Sidereal year, due to circumstances other than the primary functions governing the Earth’s rotation and revolution.
The Sidereal year is therefore the basal period for the other forms of the year. As such—presuming our premises concerning the Pyramid’s purpose to be correct—it should be the year value defined by the true circuit of the Great Pyramid’s base. Now the square circuit of the Great Pyramid’s base defines the Solar year. This square circuit touches the true Pyramid base at four points only—the four corners. The true circuit of the Pyramid’s base is the circuit of the hollowed-in perimeter of the casing base edges. This circuit is longer than the square (corner to corner) circuit defining the Solar year, and the Sidereal year is longer than the Solar year. In other words, the hollowed-in base circuit is the true constructional base circuit, as the Sidereal year is the true constructional year circuit of the basal dynamics of the Earth’s orbit. The question, then, to be settled is whether the hollowed base circuit gives the value of the Sidereal year to the scale of 100 P” to a day.
Plate XXV illustrates how the representation in plan should indicate the three values of the year. This is derived from the geometrical sequence of Plates XXIII and XXIV in relation to the geometry of the 35th course axis and the aroura. The derivation of the 35th course axis connection is illustrated on Figs. A and A1 (Plate XXV). In Fig. A1 (Plate XXV), the apex Pyramid circuit at level acb =3652.42465 P”, and this is equal to the apex Pyramid circuit D2J1D1 (Plate XXIV). The connected geometry of the latter defines the displacement of the axis of the Passage System and the displacement of the central hollowing-in of the Pyramid’s base sides. The circuit of the apex Pyramid at acb (Plate XXV, Fig. A1) is therefore equal to the 35th axis length EG=FH (Plate XXV, Fig. A). The rectangular aroura defined by the latter are EGRC and EFQC, and these are respectively equal in area to the aroura parallelograms EGBH and EFAD (the two horizontally shaded areas of Plate XXV, Fig. A). The two latter define the centrally hollowed-in area as DEH, in elevation on Fig. A, and as D1E1H1, in plan, Fig. B, Plate XXV.1 The maximum extent of hollowing-in (35.762777 P” horizontally from the geometrical plane face of the Pyramid’s slope) applies to the whole area DEH (Fig. A) , and along the line EO (Fig. A) to the base of the apex Pyramid at c (Fig. A1). The broadly fluted (or scooped-leaf) effect necessary to taper off the hollowing towards the apex is illustrated on Figs. A1 and A2 (Plate XXV).
¶ 154. THE THREE ASTRONOMICAL YEAR-CIRCUITS OF THE PYRAMID BASE. The restoration of ¶153 is the one restoration that satisfies all the structural and geometrical features of the Great Pyramid. The real test of its having been the intentional geometrical arrangement is the extent to which it satisfies the conditions postulated in. ¶¶ 150-152.
(1) That the actual (hollowed-in) structural circuit (AD1H1B, etc., in Fig. B, Plate XXV) of the Now the external geometrical base circuit, as defined, is 36,524.2465 P”, representing, to the scale defined, a good average value for the Solar year for a long period of history from ancient to modern times. The internal geometrical base circuit, as defined, and resulting from the geometry described, is 36525.997317 P”, representing, to the scale defined, a good average value for the Anomalistic year. The resulting value of 365.25997317 days for the Anomalistic year is only 33½ seconds of time longer than the value for the present time,1 365.2595844 days.
¶ 155. ASTRONOMICAL RELATIONSHIP OF THE THREE FORMS OF THE YEAR. (Plate XXV, Fig. C.)
The path or orbit of the Earth round the Sun is an ellipse, ACPB, of which F1 and F2 are the two foci. The Sun’s centre is at the focus F2. O is the centre of the orbit. AOP is the major axis, and BOC the minor axis of the elliptic orbit. The ellipse figured is considerably exaggerated as a representation of the Earth’s elliptical orbit. The latter, to any ordinary scale of representation, cannot be distinguished from a circle. When the Earth is nearest the Sun it is at P—on the major axis— whence P is called Perihelion. When the Earth is farthest from the Sun it is at A—also on the major axis—whence A is called Aphelion. The Earth travels round its orbit in the direction of the arrow, i.e. direction BACPB. Now let S be a fixed point in the heavens, and E the equinox for a particular year. Owing to a slow movement of the Earth’s axis,1 the equinox of the following year does not occur at E, but at a point E1, about 50” of angle (or 20 minutes of time) short of E. The Solar year is therefore the interval in days taken by the Earth to travel round the distance EACPBE1; whereas the Sidereal (or Stellar) year — fixed from the immovable point S, and its immovable radius F2S1S — is the interval in days taken by the Earth to travel round the distance S1PBACS1. The Solar year is therefore shorter than the Sidereal year by the interval E1E — about 50” of angle, or about 20 minutes of time. The Equinox is not, however, the only point that moves. In the course of the Earth’s revolution round its orbit, the orbit itself is not stationary, but moves round in the direction of the Earth’s revolution. In the course of one revolution of the Earth round its orbit, the major axis AF2P moves round to the position A1F2P1. Hence, commencing, say, from perihelion at P, the Earth travels round PBACPP1 to return to perihelion. This revolution defines the Anomalistic or Orbital year. It is longer than the Sidereal year by the time it takes the Earth to travel from P to P1. PP1 is about 11.5” of angle, or about 4.6 minutes of time. (Refer also Plates LV and LVI.)
F2P = the shortest distance between the Earth and Sun F2A = the longest The mean of these is OP=OA, and this distance, in astronomical nomenclature, is defined as the mean sun distance. The eccentricity of the elliptic orbit is
The value of this eccentricity (e) is variable. Its value for 1900 A.D. is 0.016751. Its greatest value during the past 60,000 years occurred about 11,600 B.C. It was then something over 0.019. Since that time it has been slowly but constantly diminishing, and will continue to diminish until about 26,000 A.D. The value of e will then be about 0.004, when the Earth’s orbit will be as nearly a circle as it is ever likely to be. To determine accurately the functions of the year, at any period, knowledge of these and other values, as well as of the laws governing motion in elliptic orbits, is a matter of fundamental necessity. Without going extensively into the subject of the Laws of Planetary Motion, attention is directed to an important corollary of these laws which has an important bearing upon the question of the Sun’s mean distance. ¶157. THE MAJOR AXIS OF THE ORBIT A DYNAMICAL CONSTANT. (Plate XXV, Fig. D.) In Fig. D, ABPC is the elliptic orbit of Fig. C, with the Sun in focus F2. The corollary to which attention is directed is as follows :— The speed of the Earth round its elliptic orbit is at every point, such as Q, equal to the speed which the Earth would acquire in falling to the ellipse at Q, from Q1 on the circumference of a circle (Q1R) with centre at the Sun (F2), and radius (F2Q1) equal to the major axis (AP) of the elliptic orbit. Thus the speed of the Earth at Q in the elliptic orbit is equal to the speed the Earth would acquire at Q in falling towards the Sun from Q1 to Q. From this it follows that “ the period “ of the Earth’s revolution round its orbit is “ independent of every element except the major axis.”1 For purpose of brevity, rather than accuracy of definition, we will term the circle Q1R the “ Earth’s Speed Circle.”
¶ 158. THE GEOMETRICAL REPRESENTATION OF THE RANGE OF VARIATIONS IN RELATION TO THE BASAL CONSTANT. The single constant geometrical feature of the Earth’s orbit is therefore the Earth’s “ Speed Circle,” with its centre occupied by the Sun. Referring again to Fig. D of Plate XXV, we see that the Earth’s orbit ABPC revolves in an anti-clockwise direction about the fixed point F2, defined as the centre of the Sun, and the centre of the Earth’s Speed Circle RQ1- Thus the point O describes a circle around F2. Points P, F1 and A on the major axis, and points B and C on the minor axis, also each describe their independent circles around F2 as centre. None of these points, then—other than the fixed centre of the Sun, F2— can be deemed as suitable for the origin of coordinates for any graphical representation of the Earth’s orbit defining the limits of its movements and variations. Nor, indeed, can the orbit for any particular date be graphically represented as defining in general geometrical terms the limiting values of orbital cycles. Now, since the distance F2O is a variable distance, and since 0 rotates around F2 as a fixed centre, it is clear that a circle of radius F2O, minimum value, and an outer circle of radius F20, maximum value, completely define the limits of variation of the centre of the orbit from the Sun. During the long period of the rotation of the orbit round the Sun (over 108,000 years) the curve traced by the centre point O of the orbit lies within the ring defined by the maximum and minimum circles. These two circles, together with the Earth’s “ Speed Circle “—all concentric with the Sun—completely define, in general geometrical terms, the fixed element of the Earth’s orbit—i.e. its major axis—and the range of variation of the variable elements. A representation of this nature is the necessary geometrical basis for any further representation defining the variable elements in relation to any standard system of astronomical chronology.
With e = eccentricity of Earth's orbit, then (fig. D of Plate XXV): -
F2O being variable within its defined limits, and F2Q1 being a constant = the major axis of the Earth’s orbit =AOP. The radius of the Earth’s “ Speed Circle “ is defined by the distance, OK, K being the intersection of the perpendiculars, AK and BK, from the converging base side lengths, AD1 and EH1 respectively. Other points such as : K are defined by all four sides of the Pyramid’s base, this definition completing the circuit of the Earth’s “Speed Circle.” The radius OK of this circle, by geometrical construction, is 470860.606 P”. The diameter VOU of the • minimum circle, by geometrical construction, is 1826.212325 P”, and the diameter of the maximum circle is 9131.061625 P”. From these values —
These values are respectively the least and the greatest possible values: of e—the eccentricity of the Earth’s orbit—as accurately as modern astronomy can determine these values. Again,
This distance, multiplied by 25,000,000
Professor Simon Newcomb1 gives for the latter a mean value of 92,998,000 miles. Thus we have found (¶¶ 101 and 114) that
and that Pyramid’s “ Speed Circle “ radius OK
For modern variations in the determination of the value of the Sun’s Mean Distance, the reader is referred to Section III, ¶ 201.
Section I. — summary and conclusions. ¶ 160. THE GEOMETRICAL EXPRESSION OF NATURAL LAW. The Great Pyramid has now clearly established its intention in regard to its inch-unit. It defines that this unit is a Polar diameter inch-unit of the value of one 5oo-millionth part of the Earth’s Polar diameter. In conjunction with a simple, yet extensive system of solid geometry, the Pyramid inch-unit, as applied to the dimensions and form of the Pyramid’s exterior, defines a further intentional representation. This is to the effect that all dimensions (angular and linear), and all motions—as well as variations in these dimensions and motions—of the Earth and its orbit, are simple functions of the Earth’s Polar diameter and of the period of the Sidereal Year in solar days. In other words, the Great Pyramid’s external system of geometry is the graphical expression of the Natural Law relationship inferred from the mathematical clue of the four Pyramid constants that defined, by the noon reflexion phenomena, the principal points of the year (¶¶ 46 and 47). The manner in which the Pyramid’s base plan simply defines the dimensions and limiting areas of dimensional variations of the Earth’s orbit shows clearly that the intention was to present these as governed by the Laws—or, as the Pyramid seems to define, an all-including Law—of Gravitation (¶¶157, 158). This comprehensive graphical representation is independent entirely of any question as to the accuracy of any survey or measurement of the Pyramid’s base, yet this independent representation agrees precisely with the accurate modern survey measurements. The intentional numerical value of the circuit of the Pyramid base square is defined in terms of the known duration of the Phoenix Cycle, or the Cycle of the House of Enoch (¶ 149). In this connection the relations established in ¶ 38 and 39 possess a remarkable numerical significance. A fact requiring emphasis, in connection with the use of the Polar diameter inch in the Pyramid, is that this unit and the year circle form the necessary basis for the derivation of the Egyptian common cubit and the Egyptian aroura. Nevertheless, the common cubit was in use in Egypt— but without the inch as a contemporary unit—before the Pyramid builders had arrived. This confirms what we have previously seen, that the early Egyptians had derived from the former civilisation a fragment of the science that the designer of the Great Pyramid knew in its entirety.
Whilst the solid geometrical relations of the Pyramid define the form of the Pyramid’s base perimeter, it is the constructional form of the latter that defines, in the plane of the base, all the principal relations of the Earth and its orbit. The Pyramid’s base perimeter is defined as a symmetrical figure formed of twelve lines. Its corners define an external square, and the lines of its perimeter from its corners, when produced to meet inside the centre of each base side, define a symmetrical figure formed of eight lines. (Plate XXV, Fig. B.) The twelve-line figure is the actual constructional base circuit of the Pyramid, and defines the Sidereal year to the scale of 100 Polar diameter inches to a day. The external square circuit of the Pyramid’s actual base corners, defines the Solar (or Tropical) year to the scale of 100 Polar diameter inches to a day. The eight-line figure defines the Anomalistic (or Orbital) year to the scale of 100 Polar diameter inches to a day (¶ 154). This is a graphical representation indicating that the Sidereal year is the actual constructional year value of orbital motion, that the Solar year is the apparent basal year value, and that the Anomalistic year is the most obscure value of the three. This is an exact representation of an astronomical truth.
The geometry of the Pyramid’s base is an exact representation of an astronomical truth, i.e. that the speed of the Earth at any point in its orbit can be determined from the following data :— (a) A circle with its centre at the focus of the Earth’s orbit occupied by the Sun, and of radius equal to the length of the major axis of the Earth’s orbit, i.e. twice the mean Sun distance ; and The Pyramid’s base geometry represents the radius and circle of (a) accurately to a scale of and defines the annular field of (b) to the same scale. The latter representation (i.e. of (b)) may be described as the definition of the orbital field of the free focus. The orbit of the free focus is completed in each cycle of about 21,000 years. The orbits of a series of such successive cycles, owing to the variation in the distance of the free focus from the helicentric focus, completely traverse the annular zone between its circle of minimum radius and its circle of maximum radius. The radius of the constant circle of (a) above precisely represents the value of the constant length of the major axis of the Earth’s orbit. Consequently, it represents the Sun’s, mean distance as half this value. The Sun’s mean distance is, therefore, represented as a radius, to the scale of
All these and other identities have been established as related identities in this chapter, and in preceding chapters. That they are intentional identities can scarcely now be doubted. But what new item of knowledge have we learned that is of any practical value, from the standpoint of the utilitarian, apart from it’s interest as pertaining to matters of scientific and archaeological curiosity? Very little, indeed, when viewed from the standpoint of any utilitarian basis. We have certainly learned that the dimensions and motions of the Earth and its orbit are all related functions of the simplest units of these dimensions and motions. This, however, we have known in a slightly different form from the Laws of Newton and Kepler. The rational development of Einstein’s Theory of Relativity now gives us reason to hope that these and the laws of other branches of science may be shown to be but varying phases of one Universal Law of Nature. The most we have learned, then, from the Pyramid’s geometry so far— taken as a whole—has not very materially advanced our knowledge of science beyond what we have already known in general terms. What we have learned may have caused us to alter our conceptions concerning the origin and development of ancient civilisations. But was this the sole reason that prompted the design and construction of a monument of the nature of the Great Pyramid ? Surely there was some utilitarian motive behind a project of this nature.1 ¶ 164. OMISSIONS THAT SUGGEST POSSIBLE MOTIVES. Let us consider, then, what are the outstanding features of the facts, from this standpoint of possible motive. The facts have proved to us that a certain stage of world civilisation, at an unknown—or hitherto supposedly undefined—period in the past had evolved a geometrical system of Natural Law, in relation to the motions of the Earth and its orbit, equal to, superior to, or more comprehensive than the modern system of expressing this Natural Law. The facts of importance in this statement of the case are that we have not yet learned anything concerning the precise, or even the approximate date of the stage of civilisation thus made known ; and that we have not yet derived a single tangible indication as to how the savants of that period discovered their facts of science—whether by methods of modern times, by methods unknown to modern times, or by the development of faculties now atrophied by long disuse. Another feature that must have become increasingly evident to the careful reader is of equal importance. This is that, in order to discover the scientific facts embodied in the Great Pyramid, it is essential that the investigator should have previous knowledge of these very facts. Was the object of the designer, then, merely to show a later civilisation that the precise science of gravitational astronomy had been known long previously ? Was this the sole object of a work so vast, and so painstakingly executed in the minutest detail ? The fact that the riddle of the Great Pyramid can only be read by one already in possession of the knowledge embodied in its design surely supplies a clear indication of a more utilitarian motive than we have so far seen.
To answer the preceding questions we must reach our objective in stages. One thing we have seen to be clear. This is that the designer of the Pyramid deemed he was projecting his knowledge into a future stage of civilisation that could interpret his intention. He foresaw that the contemporary language in which the facts could be conveyed would lose its meaning and idiomatic significance. It might be lost entirely, or at least be capable of mistranslation or misinterpretation. This foresight has certainly been justified. The design was therefore formulated, without the aid of written expression, to embody in its external features a geometrical symbolism in Earth standard measurements. This symbolism was to be interpreted in an age already in possession of the knowledge embodied in the symbolism projected. The modern elucidation of this symbolism clearly justifies the remarkable forethought that both conceived the future conditions and created the design to meet them. Forethought of this nature was never expended merely to teach a future race of mankind facts of science it already knew. We are compelled, then, to come to the conclusion that the Pyramid’s external features were designed to attract and direct attention to a further message of greater importance. Granting the forethought displayed, of what nature could this further message be? Clearly to tell the future race of mankind what it could not possibly know, or to confirm what could have no other possible physical means of being confirmed. A definitive limiting of future possible knowledge in this way can only relate to a break in the continuity of something essential to a race of mankind possessing the scientific knowledge defined; a break that had taken place before the Pyramid was built, and that could not be restored otherwise than by being passed on from the former civilisation to the then remotely future civilisation.
¶ 166. THE INDICATIONS OF A CHRONOLOGICAL CONNECTION. The inferred break in continuity can only be conceived as relating to some factor affecting the history of the previous civilisation, and related— or that should be related—to the history of the present stage of civilisation. However we look at this aspect of the problem, we are compelled to see that the primary essential for restoring the inferred relation must be of a chronological nature. This, indeed, is the one obvious connection suggested by the , Great Pyramid’s exterior. Here everything is connected with astronomical cycles, and astronomical cycles are the only possible means of affording a reliable datum for the chronological relations of two isolated periods of mankind’s history. Now there are two outstanding astronomical cycles associated with the Pyramid’s exterior. There is the cycle of the Precession of the Equinoxes, associated in the Pyramid geometry with a standard period of reference of 25,826.54 Solar years. And there is the cycle of the revolution of the Autumnal Equinox from Perihelion to Perihelion. There is also the cycle defining the variations in the eccentricity of the Earth’s orbit. In addition to these, there is a cycle not hitherto mentioned. This is a cycle defining an important feature of a very slight variation in the Ecliptic due to planetary attractions. The important feature mentioned is what is known as the instantaneous axis of rotation of the Ecliptic. This axis is analogous to the major axis of the Earth’s orbit, and, like the latter, has a slow revolution round the orbit. This movement—if its rate during the past 6000 years be taken as basis—completes a revolution of the Ecliptic in about 49,000 years.
A complete and accurate definition of the variable annual rates of any one of the cycles mentioned for every year over a long period of time covering the current years of the present chronological era and the years of a chronological era of past history would be sufficient to effect a chronological connection. It would not, however, suffice to define the representation of the values as intentional. A single representation would always be open to doubt on the grounds of accidental coincidence. There are also two other reasons why a single representation could not be accepted as certain evidence in the relation mentioned. These are — (1) That, whilst modern astronomy is very accurate in its definition of the variable annual rates over a period of 600 years of modern time, its values covering a period of 6000 years back from the present are not so reliable ; and Any chronological definition of present in relation to past history on the Great Pyramid’s geometrical system would require to satisfy these conditions.
¶ 168. THE POSSIBLE MAXIMUM DEFINITION. The most scientifically appropriate zero date of any system of astronomical chronology is the date at which longitude of Perihelion is o°. With this as basis, definition of intention, and definition of accurate knowledge of the astronomical values of rates and angles for both ancient and modern times would be completely established as follows :— (1) By the representation of a year of past time, which we term Date A, defined in relation to the date at which longitude of Perihelion was o°, and of a year of present time, which we term Date B, for which the longitude of Perihelion, defining the modern Date B, is given by the representation.
If items (1) to (5) and (8) and (9) are established, the conditions are satisfied as fully as any astronomer could desire. If item (9) is established, it will be proved that the Great Pyramid’s system of geometry is a graphical representation of Natural Law, defining the linear and angular measurements of the Earth and its orbit; defining the annual rates and periods of the cyclical motions of the Earth and its orbit; and defining a system of astronomical chronology that can be the basis of related reference for every period of highly developed stage of civilisation in the world’s history. With these items established as identities, the identities become intentional identities. With the latter established, there will be proved that a former civilisation was more highly skilled in the science of gravitational astronomy-—and therefore in the mathematical basis of the mechanical arts and sciences—than modern civilisation. And what will this mean? It will mean that it has taken man thousands of years to discover by experiment what he had originally more precisely by another surer and simpler method. It will mean, in effect, that the whole empirical basis of modern civilisation is a makeshift collection of hypotheses compared with the Natural Law basis of the civilisation of the past.
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P” = 9131.06 P” = 0141.1 B”. From this it is obvious that this distance over the two sockets was the original setting-out dimension for the corner to corner distance of the Pyramid’s base side.
= 0.54 B”.
